Nucleation barriers at corners for cubic-to-tetragonal phase transformation

2013/11/22 by Peter Bella, Bella, Peter, Michaël Goldman +1 · 1 citation
Engineering · Materials Science · #Analysis of PDEs (math.AP) #Classical Physics (physics.class-ph) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Microstructure and Mechanical Properties of Steels #Microstructure and mechanical properties #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.1311.5870

openalex publication_date 2013/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We are interested in the energetic cost of a martensitic inclusion of volume V in austenite for the cubic-to-tetragonal phase transformation. In contrast with the work of [Knüpfer, Kohn, Otto: Comm. Pure Appl. Math. 66 (2013), no. 6, 867--904], we consider domain with a corner and obtain a better scaling law for the minimal energy (E_min ∼ min(V^2/3,V^7/9)). Our predictions are in a good agreement with physical experiments where nucleation of martensite is usually observed near the corners of the specimen.

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